Alternate Interior Angles – Properties and Examples

Definition of Alternate Interior Angles
The Alternate Interior Angles Definition states that if two lines are crossed by a transversal line, then the angles formed in the opposite side of the transversal and in the inner part of the lines at the point of intersection of the lines with the transversal line define Alternate Interior Angles.  Most of the time, the two given lines will be parallel to each other. We can also define Alternate Interior Angles as those corresponding angles which are formed in the inner side of the lines at the point of intersection of a transversal line with those lines.

Properties of Alternate Interior Angles
If the two lines crossed by the transversal are not parallel, then the alternate interior angles formed at the point of intersection of the transversal line with the parallel lines do not have any relationship with one another.  They are just alternate interior angles.

If the two lines crossed by the transversal are parallel, then the alternate interior angles formed at the point of intersection of the transversal line with the parallel lines have equal angle measure.  This means all the alternate interior angles are equal in value. Thus there exists a relationship between the alternate interior angles so formed.

Alternate Interior Angles Examples
For better understanding of the alternate interior angles, let us consider an example. Consider two lines AB and CD lying parallel to each other horizontally.  If a transversal line PQ crosses the two parallel lines, it intersects the line AB at the point E and line CD at the point F. At this point of intersection, a pair of alternate interior angles is formed in the inner part of each line and on the alternate i.e. opposite side of the transversal line.  So, totally two pair of alternate interior angles are formed.

 Among the alternate interior angles, one angle will be obtuse and the other angle will be acute.
Suppose if the alternate interior angle AEF formed in the inner side of line AB is 110 degrees, then as the lines AB and CD are parallel, the alternate interior angle EFD formed in the inner side of the line CD is also 110 degrees. This is based on the property that: in case of parallel lines, the alternate interior angles are equal.  As these two angles are obtuse, the other two alternate interior angles formed will be acute angles of measure 70 degrees (i.e. 180 - 110 = 70).  Therefore, the alternate interior angles BEF = EFC = 70 degrees.